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| Home > Publications database > Incoherent scattering of slow neutrons by globular molecules in a cubic crystal |
| Book/Report | FZJ-2017-04207 |
; ;
1969
Kernforschungsanlage Jülich, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/14731
Report No.: Juel-0588-FN
Abstract: I. Calculation of Neutron Time-of-Flight Spectra : The incoherent neutron scattering by protons in organic substances can be experimentally studied in order to get the scattering law. We are interested in the information which neutron scattering gives about the dynamics of molecular crystals by comparing the experimental results with calculations of the scattering law based on a model. Such calculations must especially include the dependence of the scattering law on momentum transfer , because the measurement of this is the main advantage of neutron scattering methods over nuclear magnetic resonance and optical measurements. The incoherent differential cross section formula for one-quantum transitions in a harmonic lattice /1/ contains for a general system the eigenvectors and the eigenvalues of excited states in such a complicated way that it can hardly be used in practice to interpret the measurements. Therefore, we here restrict our attention to a simple system consisting of globular rigid molecules, the centers of mass of which form a cubic lattice. The scattering cross section for such a system has been derived in /2/, including the effect of rotational diffusion. These calculations will be briefly reviewed in section B. [...] II. Interpretation of Scattering Data for Adamantane : Adamantane ($C_{10}H_{16}$ is a globular, rather rigid molecule, crystalizing below 208°K in a tetragonal structure. Above 208°K the crystal structure is face-centered cubic and orientationally disordered. The melting point is at 540°K. In the cubic phase the crystal is plastic and the molecular rotations seem to be more or less free. This has been concluded from specific heat measurements /9/. Neutron measurements did not show broad peaks as one would expect for hindered rotations /10/. A model was developed, in which the occurrence of rotational jumps between equilibrium orientations, 90° apart and symmetric to the cubic axes of the crystal, has been assumed. However, the measurements were interpreted with some approximations made in the scattering law /2/. These approximations have now been avoided in the calculations of the time-of-flight distributions described in part I of this work. We have extended the earlier neutron measurements to larger scattering angles in order to see whether it is possible to fit a maximum portion of the data sets to the calculated curves using only one jump frequency. At first, in section B, we consider the influence of multiplescattering. Time-of-flight spectra measured at room temperature are presented in section C. Finally we discuss the temperature dependence of the jump frequency and compare it with NMR results (section D).
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